Q2 of 176 Page 21

Insert 5 geometric means between 16 and .

Let the five terms be a₁, a₂, a₃, a₄, a₅.

And,

A = 16, B

Now, these 5 terms are between A and B.

∴ A, a₁, a₂, a₃, a₄, a₅, B.

Now all of them are in GP

So we now have 7 terms in GP with the first term being 16 and seventh being 1/4.

∴ T_n = arⁿ^–1

Here T_n , a = 16 and

⇒

∴ a₁ = Ar =

a₂ = Ar² =

a₃ = Ar³ =

a₄ = Ar⁴ =

a₅ = Ar⁵ =

∴ The six GM between 16 and 1/4 are .

If p^th, q^th and r^th terms of an A.P. and G.P. are both a, b and c respectively, show that a^{b – c}b^c ^{– a} c^{a – b} = 1.

Insert 6 geometric means between 27 and .

Insert 5 geometric means between and .

Find the geometric means of the following pairs of numbers :

i. 2 and 8

ii. a³b and ab³

iii. –8 and –2